A detailed investigation of the variability of solar radiation can be proven useful towards more efficient and sustainable design of renewable resources systems. In this context, we analyze observations from Athens, Greece and we investigate the marginal distribution of the solar radiation process at a daily and hourly step, the long-term behavior based on the annual scale of the process, as well as the double periodicity (diurnal-seasonal) of the process. Finally, we apply a parsimonious double-cyclostationary stochastic model to generate hourly synthetic time series preserving the marginal statistical characteristics, the double periodicity and the dependence structure of the process.